SGVector<float64_t> CKLInference::get_derivative_wrt_kernel(const TParameter* param)
{
REQUIRE(param, "Param not set\n");
SGVector<float64_t> result;
int64_t len=const_cast<TParameter *>(param)->m_datatype.get_num_elements();
result=SGVector<float64_t>(len);
for (index_t i=0; i<result.vlen; i++)
{
SGMatrix<float64_t> dK(m_mu.vlen, m_mu.vlen);
//dK = feval(covfunc{:},hyper,x,j);
if (result.vlen==1)
dK=m_kernel->get_parameter_gradient(param);
else
dK=m_kernel->get_parameter_gradient(param, i);
result[i]=get_derivative_related_cov(dK);
result[i]*=CMath::exp(m_log_scale*2.0);
}
return result;
}
void KFKSDS_deriv_C (int *dim, double *sy, double *sZ, double *sT, double *sH,
double *sR, double *sV, double *sQ, double *sa0, double *sP0, double *dvof,
double *epshat, double *vareps, double *etahat, double *vareta,
double *r, double *N, double *dr, double *dN,
double *dahat, double *dvareps)
{
//int s, p = dim[1], mp1 = m + 1;
int i, ip1, j, k, n = dim[0], m = dim[2],
ir = dim[3], rp1 = ir + 1, nrp1 = n * rp1,
rp1m = rp1 * m, iaux, irp1m,
irsod = ir * sizeof(double), msod = m * sizeof(double),
nsod = n * sizeof(double), rp1msod = rp1 * msod;
//double invf[n], vof[n], msHsq, dfinvfsq[nrp1];
double msHsq;
std::vector<double> invf(n);
std::vector<double> vof(n);
std::vector<double> dfinvfsq(nrp1);
gsl_matrix_view Q = gsl_matrix_view_array(sQ, m, m);
gsl_vector_view Z = gsl_vector_view_array(sZ, m);
gsl_vector * Z_cp = gsl_vector_alloc(m);
gsl_matrix * ZtZ = gsl_matrix_alloc(m, m);
gsl_matrix_view maux1, maux2;
maux1 = gsl_matrix_view_array(gsl_vector_ptr(&Z.vector, 0), m, 1);
gsl_vector_memcpy(Z_cp, &Z.vector);
maux2 = gsl_matrix_view_array(gsl_vector_ptr(Z_cp, 0), 1, m);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &maux1.matrix,
&maux2.matrix, 0.0, ZtZ);
gsl_matrix * a_pred = gsl_matrix_alloc(n, m);
std::vector<gsl_matrix*> P_pred(n);
gsl_matrix * K = gsl_matrix_alloc(n, m);
gsl_vector_view K_irow;
std::vector<gsl_matrix*> L(n);
gsl_vector_view Qdiag = gsl_matrix_diagonal(&Q.matrix);
gsl_vector * Qdiag_msq = gsl_vector_alloc(m);
gsl_vector_memcpy(Qdiag_msq, &Qdiag.vector);
gsl_vector_mul(Qdiag_msq, &Qdiag.vector);
gsl_vector_scale(Qdiag_msq, -1.0);
std::vector<gsl_matrix*> da_pred(rp1);
std::vector< std::vector<gsl_matrix*> > dP_pred(n, std::vector<gsl_matrix*>(rp1));
std::vector<gsl_matrix*> dK(n);
// filtering
KF_deriv_aux_C(dim, sy, sZ, sT, sH, sR, sV, sQ, sa0, sP0,
&invf, &vof, dvof, &dfinvfsq, a_pred, &P_pred, K,
&L, &da_pred, &dP_pred, &dK);
// state vector smoothing and disturbances smoothing
gsl_matrix_view V = gsl_matrix_view_array(sV, ir, ir);
gsl_matrix_view R = gsl_matrix_view_array(sR, m, ir);
gsl_vector_view vaux;
gsl_vector *vaux2 = gsl_vector_alloc(m);
gsl_matrix *Mmm = gsl_matrix_alloc(m, m);
gsl_matrix *Mmm2 = gsl_matrix_alloc(m, m);
gsl_matrix *Mrm = gsl_matrix_alloc(ir, m);
gsl_vector_memcpy(Z_cp, &Z.vector);
gsl_matrix *r0 = gsl_matrix_alloc(n + 1, m);
gsl_vector_view r_row_t;
gsl_vector_view r_row_tp1 = gsl_matrix_row(r0, n);
gsl_vector_set_zero(&r_row_tp1.vector);
std::vector<gsl_matrix*> N0(n + 1);
N0.at(n) = gsl_matrix_calloc(m, m);
gsl_vector_view Ndiag;
gsl_vector *var_eps = gsl_vector_alloc(n);
msHsq = -1.0 * pow(*sH, 2);
//vaux = gsl_vector_view_array(invf, n);
vaux = gsl_vector_view_array(&invf[0], n);
gsl_vector_set_all(var_eps, msHsq);
gsl_vector_mul(var_eps, &vaux.vector);
gsl_vector_add_constant(var_eps, *sH);
gsl_vector *vr = gsl_vector_alloc(ir);
gsl_matrix *dL = gsl_matrix_alloc(m, m);
std::vector<gsl_matrix*> dr0(n + 1);
dr0.at(n) = gsl_matrix_calloc(rp1, m);
gsl_vector_view dr_row_t, dr_row_tp1;
std::vector< std::vector<gsl_matrix*> > dN0(n + 1, std::vector<gsl_matrix*>(rp1));
for (j = 0; j < rp1; j++)
{
(dN0.at(n)).at(j) = gsl_matrix_calloc(m, m);
}
for (i = n-1; i > -1; i--)
{
ip1 = i + 1;
iaux = (i-1) * rp1m;
irp1m = i * rp1m;
if (i != n-1) //the case i=n-1 was initialized above
r_row_tp1 = gsl_matrix_row(r0, ip1);
r_row_t = gsl_matrix_row(r0, i);
gsl_blas_dgemv(CblasTrans, 1.0, L.at(i), &r_row_tp1.vector,
0.0, &r_row_t.vector);
gsl_vector_memcpy(Z_cp, &Z.vector);
gsl_vector_scale(Z_cp, vof.at(i));
gsl_vector_add(&r_row_t.vector, Z_cp);
gsl_vector_memcpy(vaux2, &r_row_tp1.vector);
memcpy(&r[i * m], vaux2->data, msod);
N0.at(i) = gsl_matrix_alloc(m, m);
gsl_matrix_memcpy(N0.at(i), ZtZ);
gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, L.at(i), N0.at(ip1), 0.0, Mmm);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Mmm, L.at(i), invf.at(i), N0.at(i));
vaux = gsl_matrix_diagonal(N0.at(ip1));
gsl_vector_memcpy(vaux2, &vaux.vector);
memcpy(&N[i * m], vaux2->data, msod);
K_irow = gsl_matrix_row(K, i);
gsl_blas_ddot(&K_irow.vector, &r_row_tp1.vector, &epshat[i]);
epshat[i] -= vof.at(i);
epshat[i] *= -*sH;
maux1 = gsl_matrix_view_array(gsl_vector_ptr(&K_irow.vector, 0), 1, m);
maux2 = gsl_matrix_view_array(gsl_vector_ptr(Z_cp, 0), 1, m);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &maux1.matrix, N0.at(ip1),
0.0, &maux2.matrix);
vaux = gsl_vector_view_array(gsl_vector_ptr(var_eps, i), 1);
gsl_blas_dgemv(CblasNoTrans, msHsq, &maux2.matrix, &K_irow.vector,
1.0, &vaux.vector);
gsl_blas_dgemm(CblasNoTrans, CblasTrans, 1.0, &V.matrix, &R.matrix,
0.0, Mrm);
gsl_blas_dgemv(CblasNoTrans, 1.0, Mrm, &r_row_tp1.vector,
0.0, vr);
memcpy(&etahat[i*ir], vr->data, irsod);
Ndiag = gsl_matrix_diagonal(N0.at(ip1));
gsl_vector_memcpy(Z_cp, &Ndiag.vector);
gsl_vector_mul(Z_cp, Qdiag_msq);
gsl_vector_add(Z_cp, &Qdiag.vector);
gsl_blas_dgemv(CblasTrans, 1.0, &R.matrix, Z_cp, 0.0, vr);
memcpy(&vareta[i*ir], vr->data, irsod);
// derivatives
dr0.at(i) = gsl_matrix_alloc(rp1, m);
for (j = 0; j < rp1; j++)
{
k = i + j * n;
gsl_vector_memcpy(Z_cp, &Z.vector);
gsl_vector_scale(Z_cp, dvof[k]);
vaux = gsl_matrix_row(dK.at(i), j);
maux1 = gsl_matrix_view_array(gsl_vector_ptr(&vaux.vector, 0), m, 1);
maux2 = gsl_matrix_view_array(gsl_vector_ptr(&Z.vector, 0), 1, m);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, -1.0, &maux1.matrix,
&maux2.matrix, 0.0, dL);
dr_row_t = gsl_matrix_row(dr0.at(i), j);
dr_row_tp1 = gsl_matrix_row(dr0.at(ip1), j);
gsl_blas_dgemv(CblasTrans, 1.0, dL, &r_row_tp1.vector, 0.0, &dr_row_t.vector);
gsl_vector_add(&dr_row_t.vector, Z_cp);
gsl_blas_dgemv(CblasTrans, 1.0, L.at(i), &dr_row_tp1.vector, 1.0, &dr_row_t.vector);
(dN0.at(i)).at(j) = gsl_matrix_alloc(m, m);
gsl_matrix_memcpy((dN0.at(i)).at(j), ZtZ);
gsl_matrix_scale((dN0.at(i)).at(j), -1.0 * dfinvfsq.at(k));
gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, dL, N0.at(ip1), 0.0, Mmm);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Mmm, L.at(i),
1.0, (dN0.at(i)).at(j));
gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, L.at(i),
(dN0.at(ip1)).at(j), 0.0, Mmm);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Mmm, L.at(i),
1.0, (dN0.at(i)).at(j));
gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, L.at(i),
N0.at(ip1), 0.0, Mmm);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Mmm, dL,
1.0, (dN0.at(i)).at(j));
if (i != 0)
{
vaux = gsl_matrix_diagonal((dN0.at(i)).at(j));
gsl_vector_memcpy(vaux2, &vaux.vector);
memcpy(&dN[iaux + j * m], vaux2->data, msod);
}
vaux = gsl_matrix_row(da_pred.at(j), i);
gsl_blas_dgemv(CblasNoTrans, 1.0, (dP_pred.at(i)).at(j) , &r_row_t.vector,
1.0, &vaux.vector);
gsl_blas_dgemv(CblasNoTrans, 1.0, P_pred.at(i), &dr_row_t.vector,
1.0, &vaux.vector);
gsl_vector_memcpy(vaux2, &vaux.vector);
memcpy(&dahat[irp1m + j * m], vaux2->data, msod);
gsl_matrix_memcpy(Mmm, (dP_pred.at(i)).at(j));
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, -1.0, (dP_pred.at(i)).at(j),
N0.at(i), 0.0, Mmm2);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Mmm2, P_pred.at(i),
1.0, Mmm);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, -1.0, P_pred.at(i),
(dN0.at(i)).at(j), 0.0, Mmm2);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Mmm2, P_pred.at(i),
1.0, Mmm);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, -1.0, P_pred.at(i),
N0.at(i), 0.0, Mmm2);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Mmm2,
(dP_pred.at(i)).at(j), 1.0, Mmm);
gsl_matrix_mul_elements(Mmm, ZtZ);
std::vector<double> vmm(Mmm->data, Mmm->data + m*m);
dvareps[i*rp1 + j] = std::accumulate(vmm.begin(), vmm.end(), 0.0);
gsl_matrix_free((dN0.at(ip1)).at(j));
gsl_matrix_free((dP_pred.at(i)).at(j));
}
if (i != 0)
{
memcpy(&dr[iaux], (dr0.at(i))->data, rp1msod);
}
gsl_matrix_free(dr0.at(ip1));
gsl_matrix_free(dK.at(i));
gsl_matrix_free(P_pred.at(i));
gsl_matrix_free(L.at(i));
gsl_matrix_free(N0.at(ip1));
}
gsl_matrix_free(N0.at(0));
gsl_matrix_free(dr0.at(0));
for (j = 0; j < rp1; j++)
{
gsl_matrix_free((dN0.at(0)).at(j));
gsl_matrix_free(da_pred.at(j));
}
memcpy(&vareps[0], var_eps->data, nsod);
gsl_matrix_free(Mmm);
gsl_matrix_free(Mmm2);
gsl_matrix_free(Mrm);
gsl_matrix_free(r0);
gsl_matrix_free(K);
gsl_matrix_free(dL);
gsl_matrix_free(a_pred);
gsl_vector_free(Z_cp);
gsl_matrix_free(ZtZ);
gsl_vector_free(var_eps);
gsl_vector_free(vr);
gsl_vector_free(Qdiag_msq);
gsl_vector_free(vaux2);
}}